Graphene and carbon nanotubes have emerged as interesting new materials for electronics. But carbon is also a unique element for spintronics, and in particular for spin-based quantum information processing [1], because the low concentration of nuclear spins in natural carbon allows for long electron spin coherence times. We discuss the formation of quantum dots which could be used to construct a register of localized spin qubits in graphene. It turns out that both for spin relaxation and for the exchange coupling between spins, the valley degeneracy in the graphene band structure plays an essential role. The interplay of the spin and valley degrees of freedom directly manifests itself in the spin-valley blockade which has been observed in the electric transport through double quantum dots in carbon nanotubes. The second part of the talk is concerned with spin qubits based on defects in diamond, representing a different form of carbon with similarly interesting spin-related properties. We discuss all-optical electron spin qubit preparation, manipulation, and readout in a nitrogen-vacancy (NV) center in diamond [2], as well as a mechanism for storing and retrieving quantum information in the long-lived nitrogen nuclear spin [3]. Finally, we briefly present new ideas for a non-local two-qubit quantum gate between NV spins [4].